THEORY AND PRACTICE IN THE ANALYSIS OF CROSS NATIONAL AND CROSS SECTIONAL DATA: OVERVFIEW OF DIFFERENT APPROACHES

Programme “Quantitative Methods in the Social sciences” QMSS, 18-26 August 2005, University of Oxford

Organizers and Participants:

Dr Chris skinner, Prof of Social Statistics, University of Southampton

Prof Jaroslaw Gornialk, Institute of Sociology, Jagiellonian University, Krakow

Prof. Sariso , http://easr.sqp.nl

Applied Comparative Research in the Social Sciences: By Martin Kroth

Analysis of Cross national longitudinal data: By Marc Callens (CBGS, Brussels and KULeuven, Leuven)

Models for multiple group and heterogeneous data: By Albert Satorra, Univ Pompeu Fabra, Barcelona, www.econ.upff.edu/satorra


Analysis of pooled data with interaction effects
By: Germa Coenders, Dept of Economics, Univ of Girona

Moderated regression analysis MRA a particular specfification of multipkle linear regression analysis by ordinary least squares OLS which includes products of regressors has been widely used when the value of a continuous variable influences the effect of another continuous variable on the dependent one. Within comparative research, this can be understood as comparing the effect of one variable over all infinite possible values of the other variable.

Alternative ways are presented to correct for measurement error bias, which differs in:

- assumptions(sample size, normality…)
- simplicity (expertise required from the user)
- efficiency
- generalizability for complex models (e.g. models with many variables, models with indirect effects)

The issue here is one of bias and efficiency:
- introducing wrong constrains can lead to bias. Introducing correct constrains can reduce standard errors
-thus we advise practitioners to use the very simple non linear constraint if software permits
- constraints which require normality are not advised

This provides a simplified and robust specification and an extension of the usual approaches for modelling interactions using SEM

The main idea underlying the simplified approach stems from the fact that there are still very few SEM users modelling interaction effects. Researchers keep using MRA instead because SEM simply requires too much methodological expertise.

Since Kenny and Judd (1984), available approaches have involved two step methods with unclear theoretical and statistical properties, limited information methods, sophisticated methods out of reach of applied researchers or one step SEM methods with very complicated non linear constraints, some of which required normality which, according to our simulations, is a very unwise assumption. Marsh et al. (2004) proposed some important simplifications and we in some respects simplify their proposal even further (omission of the mean structure) and in some other respects extend it (inclusion of indirect effects and constraint).

The main idea underlying the extension of the approaches used so far is that by restricting SEM to one equation models, researchers were diminishing the potentiality of SEM. SEM should be able to cope with relatively complex models, including indirectly effects. The elimination of the need for complex constraints makes the approach much more workable, independent of the complexity of the model and the fulfilment of normality, while allowing applied researchers to fit these models easily.

Practical recommendations are:
To drop the mean structure
To use non overlapping indicators for the latent interaction
To introduce one constraint

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Random effects as latent variables: SEM for repeated measures data

By Dr Patrick Sturgis, Univ of Surrey

Repeated Measures and Random Effects
- a problem when analysing panel data is how to account for the correlation between observations on the same subject
- different approaches handle this problem in different ways. E.g.impose different structures on the residual correlations (exchangeable, unstructured, independent)
- assume correlations between repeated observations arise because the regression coefficients vary across subjects
- So, we have average or fixed effects for the population as a whole
And individual variability or random effects around these average coefficients
This is sometimes referred to as a random effects or multi level model

SEM for Repeated Measures

The primary focus has been on how latent variables can be used on cross sectional data
The same framework can be used on repeated measured data to overcome the correlated residuals problem
The mean of a latent variable is used to estimate to the average or fixed effect
The variance of a latent variable represents individual heterogeneity around the fixed coefficient - the random effect
For cross sectional data latent variables are specified as a function of different items at the same time point
For repeated measures data, latent variables are specified as a function of the same item at different time points

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